Sony boffins have built a battery out of paper.
The so-called "bio battery" uses enzymes to catalyse the breakdown of glucose stored within the cellulose that forms the paper's wood pulp fibres.
Sony bio battery
The battery has a structure that keeps reaction elements separate to encourage the flow of hydrogen ions and, to …

When do they start getting glucose from blood?

Not a battery

If you can power a musical juice box from the juice then it seems reasonable to think that once the original juice becomes sugar free it could be replaced with fresh sugar water or even just added sugar and it would get going again. That isn't a battery, it's a fuel cell.